Question

Number of real value of $x$ satisfying the equation, $\arctan \sqrt{x(x+1)}+\arcsin \sqrt{x(x+1)+1}=\frac{\pi }{2}$ is

• A. 0
• B. 1
• C. 2
• D. more than 2

Answer 1

Answer: (C)

$x(x+1)\ge 0\text{ and }0\le x^2+x+1\le 1$
$\Rightarrow x\ge 0\text{ or }x\le -1\text{ and }x(x+1)\le 0$
$x\le 0\text{ or }x\ge -1$
$\text{ Hence }x=0\text{ or }x=-1$